scholarly journals The Cauchy Problem for the Sobolev Type Equation of Higher Order

2018 ◽  
Vol 11 (1) ◽  
pp. 5-14 ◽  
Author(s):  
A.A. Zamyshlyaeva ◽  
◽  
E.V. Bychkov ◽  
Keyword(s):  
Cauchy Problem ◽  
Type Equation ◽  
Higher Order ◽  
Sobolev Type ◽  
The Cauchy Problem ◽  
Sobolev Type Equation

scholarly journals Inverse Problem for the Sobolev Type Equation of Higher Order

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1647
Author(s):  
Alyona Zamyshlyaeva ◽  
Aleksandr Lut
Keyword(s):  
Inverse Problem ◽  
Bounded Operator ◽  
Type Equation ◽  
Higher Order ◽  
Successive Approximations ◽  
Unknown Coefficient ◽  
Method Of Successive Approximations ◽  
Sobolev Type ◽  
Equivalent Problems ◽  
Sobolev Type Equation

The article investigates the inverse problem for a complete, inhomogeneous, higher-order Sobolev type equation, together with the Cauchy and overdetermination conditions. This problem was reduced to two equivalent problems in the aggregate: regular and singular. For these problems, the theory of polynomially bounded operator pencils is used. The unknown coefficient of the original equation is restored using the method of successive approximations. The main result of this work is a theorem on the unique solvability of the original problem. This study continues and generalizes the authors’ previous research in this area. All the obtained results can be applied to the mathematical modeling of various processes and phenomena that fit the problem under study.

scholarly journals The Cauchy problem for a higher order shallow water type equation on the circle

2015 ◽  
Vol 259 (9) ◽  
pp. 4863-4896 ◽  
Author(s):  
Shiming Li ◽  
Wei Yan ◽  
Yongsheng Li ◽  
Jianhua Huang
Keyword(s):  
Cauchy Problem ◽  
Shallow Water ◽  
Type Equation ◽  
Higher Order ◽  
Water Type ◽  
The Cauchy Problem

scholarly journals Optimal Control of Solutions to the Initial-Final Problem for the Sobolev Type Equation of Higher Order

2016 ◽  
Vol 3 (2) ◽  
pp. 57-67 ◽  
Author(s):  
A.A. Zamyshlyaeva ◽  
◽  
O.N. Tsyplenkova ◽  
E.V. Bychkov ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Type Equation ◽  
Higher Order ◽  
Sobolev Type ◽  
Sobolev Type Equation

scholarly journals The Cauchy Problem for Higher-Order KP Equations

1999 ◽  
Vol 153 (1) ◽  
pp. 196-222 ◽  
Author(s):  
J.C. Saut ◽  
N. Tzvetkov
Keyword(s):  
Cauchy Problem ◽  
Higher Order ◽  
The Cauchy Problem ◽  
Kp Equations

On the classical solutions for a Rosenau–Korteweg-deVries–Kawahara type equation

2021 ◽  
pp. 1-23
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
Cauchy Problem ◽  
Small Amplitude ◽  
Type Equation ◽  
Discrete Systems ◽  
Finite Depth ◽  
Capillary Waves ◽  
Classical Solutions ◽  
Well Posedness ◽  
Kawahara Equation ◽  
The Cauchy Problem

The Rosenau–Korteweg-deVries–Kawahara equation describes the dynamics of dense discrete systems or small-amplitude gravity capillary waves on water of a finite depth. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem.

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